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Macroeconomic Dynamics, 20, 2016, 466481. Printed in the United States of America. doi:10.1017/S1365100514000066
JESS BENHABIB AND ALBERTO BISIN
New York University
SHENGHAO ZHU
National University of Singapore
We study the dynamics of the distribution of wealth in an economy with innitely lived agents, intergenerational transmission of wealth, and redistributive scal policy. We show that wealth accumulation with idiosyncratic investment risk and uncertain lifetimes can generate a double Pareto wealth distribution.
Keywords: Wealth Distribution, Rate of Return Risk, Fat Tails
1. INTRODUCTION
The wealth distribution in the United States has a fat tail. Wolff (2006), using the 2001 Survey of Consumer Finances, nds that the top 1% of households hold 33.4% of the wealth in the United States. Investigating a sample of the richest individuals in the United States, the Forbes 400 data for 19882003, Klass et al. (2006) nd that the top end of the wealth distribution obeys a Pareto law with an average exponent of 1.49.
In this paper we study a model of wealth accumulation with idiosyncratic investment risk and uncertain lifetime and show that it can generate a double Pareto wealth distribution displaying a Pareto upper tail.1
Our model is a continuous-time OLG heterogeneous-agents model. There is a continuum of agents with measure 1 in the economy. Agents have uncertain lifetimes with constant probability of death at each point. The agents have joy of giving bequest motives and allocate their wealth among current consumption, a risky asset, a riskless asset, and the purchase of life insurance. The risky asset is a private investment project whose value follows a geometric Brownian motion. Returns from the private investment projects are subject to idiosyncratic risk. The returns from riskless assets and life insurance are the same for all agents. The government taxes capital income and redistributes the proceeds as means-tested subsidies.
The agents optimal wealth accumulation process follows a geometric Brownian motion and we can calculate the growth rate of aggregate wealth. The ratio
Address correspondence to: Jess Benhabib, Department of Economics, New York University, 19 West 4th Street, 6th Floor, New York, NY 10012, USA; e-mail: [email protected].
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[circlecopyrt] 2014 Cambridge University Press 1365-1005/14 466
THE DISTRIBUTION OF WEALTH IN THE BLANCHARDYAARI MODEL
DISTRIBUTION OF WEALTH IN THE BLANCHARDYAARI MODEL 467
of individual...